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A shocked friend of Ms Pert told the Herald today she was a "kind and gentle person".

Dr Rona Wang became Ms Pert's friend when she was teaching her at the New Zealand School of Acupuncture and Traditional Chinese Medicine. Ms Pert had been studying for her Health Science masters degree in Traditional Chinese Medicine.

Dr Wang said it was "very sad news".

"She was so very kind and beautiful. A very intelligent woman with much knowledge," Dr Wang said.

"She was a great mum to her daughter and son, I am thinking of her family."

Dr Wang, a gynaecologist and pediatrician, said Ms Pert became interested in Chinese medicine when she was pregnant and had some growth issues.

Family of Ms Pert travelled to Auckland today and met police investigating her death.

At the Whanganui home of Ms Pert's parents this afternoon, a visibly upset man said they did not have any comment.

Ms Pert's father, Kevin Pert, earlier told Fairfax he was "totally in shock" after he was told of his daughter's death yesterday.

He described his daughter as a "fantastic mother".

"She was also a great sportsperson and super-qualified. She was an accountant and had a medical degree," he told Fairfax.

Ms Pert had been on a regular run in Remuera when she was attacked, he said.

"She was just in the wrong place at the wrong time."

In a statement released this afternoon, police said the family met Detective Inspector Kevin Hooper and staff from the homicide investigation team.

Mr Hooper said the Operation Solitaire homicide investigation team had a lot of work to do piecing together the events before and after Ms Pert's death.

"Our sympathies are obviously with Joanne's family and friends and we are committed to making every effort to ensure a robust prosecution is achieved. Staff were back at the Shore Rd scene earlier today and others are carrying out background inquiries into the accused."

Several other inquiries will take weeks to complete, he said.

"We are relieved that we are able to reassure members of the community that the alleged offender acted alone and is remanded in custody."

The occupants of the property where Ms Pert was found have returned to their home. They would not comment when approached today.

Ms Pert's name was suppressed this morning when the man charged with her murder appeared in the Auckland District Court. The suppression lapsed at 4pm.

The 24-year-old Mount Roskill accused was remanded in custody until his next appearance in the High Court in Auckland on January 27. His name suppression will be revisited then.

He appeared wearing a blue boiler suit.

Judge Claire Ryan ordered a number of reports including a psychiatric evaluation.The accused did not apply for bail.

He appeared calm during the short hearing. He smiled once towards the end of the appearance.

Ms Pert was either walking or jogging along Shore Rd when she was allegedly attacked and killed by the Auckland man yesterday.

The stranger allegedly used a weapon to fatally attack her, and she tried to get help at a nearby house.

She collapsed on the front lawn of a house, just metres from the front door.

Some time later - possibly more than an hour - the occupants saw her from their window and called for help.

Emergency services were called just before 11am.

The man walked into the Auckland Central police station at midday and surrendered.

He carried with him a weapon which police believe he used to kill the woman.